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Bayesian graphical models have been shown to be a powerful tool for discovering uncertainty and causal structure from real-world data in many application fields. Current inference methods primarily follow different kinds of trade-offs…

The Hamiltonian Monte Carlo (HMC) algorithm is often lauded for its ability to effectively sample from high-dimensional distributions. In this paper we challenge the presumed domination of HMC for the Bayesian analysis of GLMs. By utilizing…

Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…

Consider one realization of a continuous-time Gaussian process $Z$ which belongs to the Mat\' ern family with known ``regularity'' index $\nu >0$. For estimating the autocorrelation-range and the variance of $Z$ from $n$ observations on a…

In this paper, we first propose a Bayesian neighborhood selection method to estimate Gaussian Graphical Models (GGMs). We show the graph selection consistency of this method in the sense that the posterior probability of the true model…

In the popular approach of "Bayesian variable selection" (BVS), one uses prior and posterior distributions to select a subset of candidate variables to enter the model. A completely new direction will be considered here to study BVS with a…

Selecting between different dependency structures of hidden Markov random field can be very challenging, due to the intractable normalizing constant in the likelihood. We answer this question with approximate Bayesian computation (ABC)…

A new methodology for model determination in decomposable graphical Gaussian models is developed. The Bayesian paradigm is used and, for each given graph, a hyper inverse Wishart prior distribution on the covariance matrix is considered.…

Elliptical slice sampling is a widely used gradient-free Markov chain Monte Carlo algorithm that is tuning-free and capable of adapting to local characteristics of the target distribution. However, its primary limitation is that sampling…

This paper presents a Bayesian inference framework for a linear index threshold-crossing binary choice model that satisfies a median independence restriction. The key idea is that the model is observationally equivalent to a probit model…

Identifying the active factors that have significant impacts on the output of the complex system is an important but challenging variable selection problem in computer experiments. In this paper, a Bayesian hierarchical Gaussian process…

We investigate how ideas from covariance localization in numerical weather prediction can be used in Markov chain Monte Carlo (MCMC) sampling of high-dimensional posterior distributions arising in Bayesian inverse problems. To localize an…

Graphical model selection in Markov random fields is a fundamental problem in statistics and machine learning. Two particularly prominent models, the Ising model and Gaussian model, have largely developed in parallel using different (though…

This paper considers the objective comparison of stochastic models to solve inverse problems, more specifically image restoration. Most often, model comparison is addressed in a supervised manner, that can be time-consuming and partly…

We develop a Bayesian spatio-temporal framework for extreme-value analysis that augments a hierarchical copula model with an autoregressive factor to capture residual temporal dependence in threshold exceedances. The factor can be specified…

In this paper, we study Bayesian approach for solving large scale linear inverse problems arising in various scientific and engineering fields. We propose a fused $L_{1/2}$ prior with edge-preserving and sparsity-promoting properties and…

Spike-and-slab and horseshoe regression are arguably the most popular Bayesian variable selection approaches for linear regression models. However, their performance can deteriorate if outliers and heteroskedasticity are present in the…

Latent factor GARCH models are difficult to estimate using Bayesian methods because standard Markov chain Monte Carlo samplers produce slowly mixing and inefficient draws from the posterior distributions of the model parameters. This paper…

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

In this paper we propose a new Bayesian estimation method to solve linear inverse problems in signal and image restoration and reconstruction problems which has the property to be scale invariant. In general, Bayesian estimators are {\em…